{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import atomman as am\n",
    "import atomman.unitconvert as uc\n",
    "import atomman.lammps as lmp\n",
    "import numpy as np\n",
    "from copy import deepcopy\n",
    "import potentials\n",
    "import datetime\n",
    "import iprPy\n",
    "\n",
    "from pathlib import Path\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Bain():\n",
    "    \n",
    "    def __init__(self, a_bcc, a_fcc, symbol):\n",
    "        \n",
    "        # Define prototype bcc ucell\n",
    "        self.__proto = am.System(atoms=am.Atoms(pos=[[0.0, 0.0, 0.0], [0.5, 0.5, 0.5]]), symbols=symbol)\n",
    "        \n",
    "        self.a_bcc = a_bcc\n",
    "        self.a_fcc = a_fcc\n",
    "\n",
    "    @property\n",
    "    def proto(self):\n",
    "        return self.__proto\n",
    "        \n",
    "    @property\n",
    "    def a_bcc(self):\n",
    "        return self.__a_bcc\n",
    "    \n",
    "    @a_bcc.setter\n",
    "    def a_bcc(self, value):\n",
    "        self.__a_bcc = float(value)\n",
    "    \n",
    "    @property\n",
    "    def a_fcc(self):\n",
    "        return self.__a_fcc\n",
    "    \n",
    "    @a_fcc.setter\n",
    "    def a_fcc(self, value):\n",
    "        self.__a_fcc = float(value)\n",
    "    \n",
    "    def ucell(self, a_scale, c_scale):\n",
    "        \n",
    "        # Get the ideal deformation points\n",
    "        a_0 = self.a_fcc * 2**0.5 / 2\n",
    "        c_0 = self.a_fcc\n",
    "        a_1 = c_1 = self.a_bcc\n",
    "        \n",
    "        a = a_0 * (1 - a_scale) + a_1 * a_scale\n",
    "        c = c_0 * (1 - c_scale) + c_1 * c_scale\n",
    "        \n",
    "        ucell = deepcopy(self.proto)\n",
    "        ucell.box_set(a=a, b=a, c=c, scale=True)\n",
    "        \n",
    "        return ucell\n",
    "    \n",
    "    def itercellmap(self, num_a=23, num_c=23, min_a=-0.05, max_a=1.05, min_c=-0.05, max_c=1.05):\n",
    "        \n",
    "        \n",
    "        # Construct mesh of regular points\n",
    "        avals, cvals = np.meshgrid(np.linspace(min_a, max_a, num_a),\n",
    "                                   np.linspace(min_c, max_c, num_c))\n",
    "        \n",
    "        for a, c in zip(avals.flat, cvals.flat):\n",
    "            yield a, c, self.ucell(a, c)\n",
    "            \n",
    "    def set_results(self, a_scale, c_scale, E_coh):\n",
    "        d = int(len(results['a_scale'])**0.5)\n",
    "        \n",
    "        self.a_scale = np.array(a_scale)\n",
    "        self.c_scale = np.array(c_scale)\n",
    "        self.E_coh = np.array(E_coh)\n",
    "        \n",
    "    def plot_1d_path(self):\n",
    "        \n",
    "        fig = plt.figure(figsize=(8,5))\n",
    "        \n",
    "        matches = (self.a_scale == self.c_scale)\n",
    "        plt.plot(self.a_scale[matches], self.E_coh[matches])\n",
    "        plt.xlabel('linear deformation coefficient: 0=fcc, 1=bcc')\n",
    "        plt.ylabel('Cohesive energy (eV/atom)')\n",
    "        \n",
    "        return fig\n",
    "    \n",
    "    def plot_2d(self):\n",
    "        \n",
    "        fig = plt.figure(figsize=(10,8))\n",
    "        \n",
    "        d = int(len(self.a_scale.flat)**0.5)\n",
    "        a_scale = self.a_scale.reshape(d,d)\n",
    "        c_scale = self.c_scale.reshape(d,d)\n",
    "        E_coh = self.E_coh.reshape(d,d)\n",
    "        plt.pcolormesh(a_scale, c_scale, E_coh)\n",
    "        plt.xlabel('xy linear deformation coefficient')\n",
    "        plt.xlabel('z linear deformation coefficient')\n",
    "        cbar = plt.colorbar()\n",
    "        cbar.ax.set_ylabel('cohesive energy (eV/atom)',\n",
    "                           fontsize='x-large')\n",
    "        plt.show()\n",
    "        \n",
    "        return fig\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('min.template', 'w') as f:\n",
    "    f.write(\"\"\"#LAMMPS input script that performs a simple energy minimization\n",
    "\n",
    "<atomman_system_pair_info>\n",
    "\n",
    "thermo_style custom step lx ly lz pxx pyy pzz pe\n",
    "thermo_modify format float %.13e\n",
    "\n",
    "compute peatom all pe/atom \n",
    "\n",
    "min_modify dmax <dmax>\n",
    "\n",
    "dump dumpit all custom <maxeval> <sim_directory>*.dump id type x y z c_peatom\n",
    "dump_modify dumpit format <dump_modify_format>\n",
    "minimize <etol> <ftol> <maxiter> <maxeval>\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def baintransformation(a_bcc, a_fcc, symbol, sizemults, potential, lammps_command, mpi_command=None,\n",
    "                       num_a=23, num_c=23, min_a=-0.05, max_a=1.05, min_c=-0.05, max_c=1.05,\n",
    "                       etol=0.0, ftol=1e-6, maxiter=100000, maxeval=100000,\n",
    "                       dmax=uc.set_in_units(0.01, 'angstrom')):\n",
    "    \n",
    "    # Build filedict if function was called from iprPy\n",
    "    try:\n",
    "        assert __name__ == pkg_name\n",
    "        calc = iprPy.load_calculation(calculation_style)\n",
    "        filedict = calc.filedict\n",
    "    except:\n",
    "        filedict = {}\n",
    "    \n",
    "    # Get lammps units\n",
    "    lammps_units = lmp.style.unit(potential.units)\n",
    "    \n",
    "    # Get lammps version date\n",
    "    lammps_date = lmp.checkversion(lammps_command)['date']\n",
    "    \n",
    "    # Get lammps template\n",
    "    template_file = 'min.template'\n",
    "    template = iprPy.tools.read_calc_file(template_file, filedict)\n",
    "    \n",
    "    # Define constant lammps variables\n",
    "    lammps_variables = {}\n",
    "    lammps_variables['etol'] = etol\n",
    "    lammps_variables['ftol'] = uc.get_in_units(ftol, lammps_units['force'])\n",
    "    lammps_variables['maxiter'] = maxiter\n",
    "    lammps_variables['maxeval'] = maxeval\n",
    "    lammps_variables['dmax'] = uc.get_in_units(dmax, lammps_units['length'])\n",
    "    \n",
    "    # Set dump_modify format based on dump_modify_version\n",
    "    if lammps_date < datetime.date(2016, 8, 3):\n",
    "        lammps_variables['dump_modify_format'] = '\"%i %i %.13e %.13e %.13e %.13e\"'\n",
    "    else:\n",
    "        lammps_variables['dump_modify_format'] = 'float %.13e'\n",
    "    \n",
    "    # Define bain object\n",
    "    bain = Bain(a_bcc=a_bcc, a_fcc=a_fcc, symbol=symbol)\n",
    "    \n",
    "    energies = []\n",
    "    a_scales = []\n",
    "    c_scales = []\n",
    "    i = 0\n",
    "    # Iterate over cells\n",
    "    for a_scale, c_scale, ucell in bain.itercellmap(num_a=num_a, num_c=num_c, min_a=min_a,\n",
    "                                                   max_a=max_a, min_c=min_c, max_c=max_c):\n",
    "    \n",
    "        system = ucell.supersize(*sizemults)\n",
    "    \n",
    "        sim_directory = Path(str(i))\n",
    "        if not sim_directory.is_dir():\n",
    "            sim_directory.mkdir()\n",
    "        sim_directory = sim_directory.as_posix()+'/'\n",
    "            \n",
    "        # Define lammps variables\n",
    "        system_info = system.dump('atom_data', f=Path(sim_directory, 'atom.dat').as_posix(),\n",
    "                                  potential=potential,\n",
    "                                  return_pair_info=True)\n",
    "        lammps_variables['atomman_system_pair_info'] = system_info\n",
    "        lammps_variables['sim_directory'] = sim_directory\n",
    "        \n",
    "        # Write lammps input script\n",
    "        lammps_script = Path(sim_directory, 'min.in')\n",
    "        with open(lammps_script, 'w') as f:\n",
    "            f.write(iprPy.tools.filltemplate(template, lammps_variables,\n",
    "                                             '<', '>'))\n",
    "        # Run LAMMPS\n",
    "        output = lmp.run(lammps_command, lammps_script.as_posix(), mpi_command,\n",
    "                         logfile=Path(sim_directory, 'log.lammps').as_posix())\n",
    "\n",
    "        # Extract output values\n",
    "        thermo = output.simulations[-1]['thermo']\n",
    "        E_total = uc.set_in_units(thermo.PotEng.values[-1],\n",
    "                                  lammps_units['energy'])\n",
    "        a_scales.append(a_scale)\n",
    "        c_scales.append(c_scale)\n",
    "        energies.append(E_total / system.natoms)\n",
    "        \n",
    "        i += 1\n",
    "    \n",
    "    # Return results\n",
    "    results_dict = {}\n",
    "    results_dict['a_scale'] = a_scales\n",
    "    results_dict['c_scale'] = c_scales\n",
    "    results_dict['E_coh'] = energies\n",
    "    \n",
    "    return results_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_bcc=2.8665\n",
    "a_fcc=3.6057"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "potdb = potentials.Database(localpath='C:/Users/lmh1/Documents/library')\n",
    "potential = potdb.get_lammps_potential(id='2006--Chamati-H--Fe--LAMMPS--ipr1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = baintransformation(a_bcc, a_fcc, 'Fe', (3, 3, 3), potential, 'lmp_mpi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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       "  -3.882137357312222,\n",
       "  -3.9255425248496296,\n",
       "  -3.9657202330974077,\n",
       "  -4.002749668069074,\n",
       "  -4.036769588885371,\n",
       "  -4.067957058572962,\n",
       "  -4.096498472887222,\n",
       "  -4.122572570958888,\n",
       "  -4.146338807191111,\n",
       "  -4.167930381342778,\n",
       "  -4.187452601621481,\n",
       "  -4.204985861520185,\n",
       "  -4.220591362357778,\n",
       "  -4.234313483628889,\n",
       "  -4.246179244103333,\n",
       "  -4.256204432365,\n",
       "  -4.264399494427592,\n",
       "  -4.270775302092037,\n",
       "  -4.2753488376409265,\n",
       "  -4.2781443201420375,\n",
       "  -4.279192909360185,\n",
       "  -4.278528337513148,\n",
       "  -4.276181525232593,\n",
       "  -3.822684270506111,\n",
       "  -3.8710154492461117,\n",
       "  -3.915899325351296,\n",
       "  -3.9574035565770376,\n",
       "  -3.995659818873889,\n",
       "  -4.030843679109815,\n",
       "  -4.063144179991852,\n",
       "  -4.092744987260185,\n",
       "  -4.119812271979074,\n",
       "  -4.144487349942037,\n",
       "  -4.166884691633705,\n",
       "  -4.1870945925035175,\n",
       "  -4.2051887995938895,\n",
       "  -4.221227063450185,\n",
       "  -4.235259562682407,\n",
       "  -4.2473244049812955,\n",
       "  -4.257451355652963,\n",
       "  -4.265666101197962,\n",
       "  -4.271994471288333,\n",
       "  -4.276467635583147,\n",
       "  -4.2791230695907405,\n",
       "  -4.280000069348148,\n",
       "  -4.279134257130741,\n",
       "  -3.7555044769685186,\n",
       "  -3.8091735083775924,\n",
       "  -3.8591602490712966,\n",
       "  -3.905519506814815,\n",
       "  -3.9483748524894446,\n",
       "  -3.9878993753392593,\n",
       "  -4.024284391613149,\n",
       "  -4.057718393017592,\n",
       "  -4.088374373577962,\n",
       "  -4.116402030196482,\n",
       "  -4.1419254066170375,\n",
       "  -4.165045233768704,\n",
       "  -4.185844268205556,\n",
       "  -4.2043936890442595,\n",
       "  -4.220758951972037,\n",
       "  -4.235001507183334,\n",
       "  -4.247174314425,\n",
       "  -4.257323218939074,\n",
       "  -4.265490048999074,\n",
       "  -4.27171578291037,\n",
       "  -4.276045222239074,\n",
       "  -4.278524276762777,\n",
       "  -4.279194373174814]}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "bain = Bain(a_bcc=a_bcc, a_fcc=a_fcc, symbol='Fe')\n",
    "bain.set_results(**results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bain.plot_1d_path()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bain.plot_2d()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
